Pappus Alexandrinus, Mathematical Collection, Book 8, 1876

List of thumbnails

< >
1
1 		2
2
3
3 		4
4
5
5 		6
6
7
7 		8
8
9
9 		10
10
< >
page |< < of 58 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p>
              <s id="id.000015">
                <pb n="1030"/>
              </s>
            </p>
            <p>
              <s id="id.000016">Τί μὲν οὖν ἐστιν τὸ βαρὺ καὶ τὸ κοῦφον, καὶ τίς αἰ-
                <lb n="1"/>
              τία τῆς ἄνω καὶ κάτω τοῖς σώμασι φορᾶς, καὶ αὐτό γε τὸ
                <lb n="2"/>
              ἄνω καὶ κάτω τίνος ἐννοίας ἔχεται καὶ τίσιν ἀφώρισται
                <lb n="3"/>
              πέρασιν, οὐδὲν δεῖ λέγεσθαι παρ' ἡμῶν τὸ νῦν, ἐπειδὴ
                <lb n="4"/>
              περὶ τούτων ἐν τοῖς μαθηματικοῖς ὑπὸ τοῦ Πτολεμαίου
                <lb n="5"/>
              δεδήλωται, τὸ δὲ κέντρον τοῦ βάρους ἐκάστου σώματος,
                <lb n="6"/>
              ὃ τῆς κεντροβαρικῆς πραγματείας ἀρχὴ καὶ στοιχεῖόν ἐστιν,
                <lb n="7"/>
              ἐξ ἧς καὶ τὰ λοιπὰ μέρη τῆς μηχανικῆς ἀνήρτηται, τί ποτ'
                <lb n="8"/>
              ἐστὶν καὶ τί βούλεται λεκτέον· ἐκ τούτου γάρ, οἶμαι, καὶ
                <lb n="9"/>
              τὰ λοιπὰ τῶν ἐν τῇ πραγματείᾳ θεωρουμένων ἔσται σαφῆ.
                <lb n="10"/>
              </s>
              <s id="id.000017">λέγομεν δὲ κέντρον βάρους ἑκάστου σώματος εἶναι σημεῖόν
                <lb n="11"/>
              τι κείμενον ἐντός, ἀφ' οὗ κατ' ἐπίνοιαν ἀρτηθὲν τὸ βάρος
                <lb n="12"/>
              ἠρεμεῖ φερόμενον καὶ φυλάσσει τὴν ἐξ ἀρχῆς θέσιν [οὐ μὴ
                <lb n="13"/>
              περιτρεπόμενον ἐν τῇ φορᾷ]. </s>
              <s id="id.000018">τοῦτο δὲ τὸ σημεῖον οὐ
                <lb n="14"/>
              μόνον ἐν τοῖς τεταγμένοις ἀλλὰ κἀν τοῖς ἀτάκτως ἐσχη-
                <lb n="15"/>
              ματισμένοις εὑρίσκεται σώμασιν ὑπάρχον, ἐφόδῳ τινὶ θεω-
                <lb n="16"/>
              ρούμενον τοιαύτῃ.
                <lb n="17"/>
              </s>
            </p>
            <p>
              <s id="id.000019">α#. </s>
              <s id="id.000020">Ὑποκείσθω γὰρ ἐπίπεδον ὀρθὸν τὸ ΑΒΓΔ νεῦον εἰς
                <lb n="18"/>
              τὸ τοῦ παντὸς κέντρον, ἐφ' ὃ καὶ τὰ βάρος ἔχοντα πάντα
                <lb n="19"/>
              τὴν ῥοπὴν ἔχειν δοκεῖ, καὶ ἔστω ἡ ΑΒ εὐθεῖα παράλληλος
                <lb n="20"/>
              τῷ ἐφ' οὗ βεβήκαμεν ἐπιπέδῳ. </s>
              <s id="id.000021">ἐὰν δή τι τῶν βάρος ἐχόν-
                <lb n="21"/>
              των σωμάτων τιθῆται κατὰ τῆς ΑΒ εὐθείας οὕτως, ὥστε
                <lb n="22"/>
              τετμῆσθαι πάντως ὑπὸ τοῦ ἐπιπέδου ἐκβαλλομένου, ἕξει
                <lb n="23"/>
              ποτὲ θέσιν τοιαύτην, ὥστε μένειν ἀπερίτρεπτον καὶ μὴ
                <lb n="24"/>
              ἀποπίπτειν. </s>
              <s id="id.000022">γενομένου δὲ τούτου ἐὰν νοηθῇ τὸ ΑΒΓΔ ἐπί-
                <lb n="25"/>
              πεδον ἐκβαλλόμενον, τεμεῖ τὸ ἐπικείμενον σῶμα εἰς ἰσόρ-
                <lb n="26"/>
              ροπα δύο μέρη, οἷον περὶ ἄρτημα τὸ ἐπίπεδον ἰσορρο-
                <lb n="27"/>
              ποῦντα. </s>
              <s id="id.000023">πάλιν δὴ τὸ βάρος μετατεθέν, ὥστε καθ' ἕτερον
                <lb n="28"/>
              μέρος ψαύειν τῆς ΑΒ εὐθείας, ἕξει ποτὲ θέσιν περιτρεπό-
                <lb n="29"/>
              μενον ὥστε μένειν ἀφεθὲν καὶ μὴ ἀποπίπτειν. </s>
              <s id="id.000024">ἐὰν οὖν
                <lb n="30"/>
              πάλιν νοηθῇ τὸ ΑΒΓΔ ἐπίπεδον ἐκβεβλημένον, εἰς ἰσορρο-
                <lb n="31"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum